F. Gagel et K. Maschke, DC MAGNETOTRANSPORT AND HALL-EFFECT IN MULTIPLY CONNECTED QUANTUM-WIRE SYSTEMS, Physical review. B, Condensed matter, 49(24), 1994, pp. 17170-17176
In the Landauer-Buttiker approach, the dc-transport properties of a sy
stem are expressed in terms of its scattering matrix. We propose a met
hod to sum the multiple-scattering events for an arbitrary ensemble of
interconnected scatterers, which leads to a closed analytic expressio
n for the matrix elements of the overall-scattering matrix. This appro
ach is used to investigate the dc magnetotransport of a planar periodi
c lattice of interconnected quantum wires. The calculated conductance
as well as the Hall voltage depend strongly on the Fermi wave vector a
nd on the magnetic field. This behavior is a consequence of the interf
erence between waves traveling along different scattering paths. It is
closely related to the eigenvalue spectrum of electrons in a two-dime
nsional lattice in the presence of a perpendicular magnetic field, whi
ch is described by the Hofstadter butterfly. We present a detailed ana
lysis of the observed features of the Hall voltage.